A background process from Brother Industries, the Brother Popup Suspend Service runs in conjunction with the Brother MFL-PRO Resource Manager and suspends popup messages from your Brother software until they are acknowledged. The Brother Resource Manager can be accessed through the Windows system tray and allows you to manage various settings for your Brother printer devices. Brother was founded in 1908 as a sewing and typewriter company, but expanded their business to include computer peripherals in the 1970s. Currently, Brother Industries manufactures a line of computer printers as their primary business.
If you want a detailed security rating about your Brmfrmps.exe (and all other running background processes) read the following user opinions, and download the free trial version of Security Task Manager.

Note: Any malware can be named anything - so you should check where the files of the running processes are located on your disk.
If a "non-Microsoft" .exe file is located in the C:\Windows or C:\Windows\System32 folder, then there is a high risk for a virus, spyware, trojan or worm infection!
Check it out!